simulation of fully grouted rockbolts in underground roadways usi
DESCRIPTION
Rockbolts, groutingTRANSCRIPT
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University of WollongongResearch Online
Faculty of Engineering and Information Sciences -Papers Faculty of Engineering and Information Sciences
2014
Simulation of fully grouted rockbolts inunderground roadways using FLAC2DShuqi MaUniversity of Wollongong, [email protected]
Jan NemcikUniversity of Wollongong, [email protected]
Naj AzizUniversity of Wollongong, [email protected]
Research Online is the open access institutional repository for theUniversity of Wollongong. For further information contact the UOWLibrary: [email protected]
Publication DetailsMa, S., Nemcik, J. & Aziz, N. (2014). Simulation of fully grouted rockbolts in underground roadways using FLAC2D. CanadianGeotechnical Journal, 51 (8), 911-920.
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Simulation of fully grouted rockbolts in underground roadways usingFLAC2D
AbstractA numerical modelling approach of a mine roadway reinforced with fully encapsulated rockbolts is proposedto study the interaction between rockbolts and the rock mass. The rockbolt bond-slip relationships defined byconducting push tests of short rockbolts are implemented in the rockbolt elements used in the two-dimensional Fast Lagrangian Analysis of Continua (FLAC2D) model for precise simulation of the rockboltbehaviour. The performance of rockbolts installed in the roadway model under various conditions is discussedand compared with previous research. This paper provides a numerical modelling methodology to study theinteraction between rockbolts and the rock mass subject to a variable stress state, rock mass quality, and thepresence of rock fractures or joints. It was found that the bearing plates can improve the reinforcingperformance of rockbolts. Copyright 2014 Published by NRC Research Press
Keywordsroadways, underground, rockbolts, grouted, fully, flac2d, simulation
Publication DetailsMa, S., Nemcik, J. & Aziz, N. (2014). Simulation of fully grouted rockbolts in underground roadways usingFLAC2D. Canadian Geotechnical Journal, 51 (8), 911-920.
This journal article is available at Research Online: http://ro.uow.edu.au/eispapers/3017
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Simulation of fully grouted rockbolts in underground roadways
using FLAC2D
Shuqi Ma, Jan Nemcik*, Naj Aziz
School of Civil, Mining and Environmental Engineering, University of Wollongong, NSW
2522, Australia
Abstract:
A numerical modelling approach of a mine roadway reinforced with fully encapsulated
rockbolts is proposed to study the interaction between the rockbolts and the rock mass. The
rockbolt bond-slip relationships defined by conducting push tests of short rockbolts are
implemented in the rockbolt elements used in the two-dimensional Fast Lagrangian Analysis
of Continua (FLAC2D) model for precise simulation of the rockbolt behaviour. The
performance of rockbolts installed in the roadway model under various conditions was
discussed and compared with the previous research. This paper provides a numerical
modelling methodology to study the interaction between rockbolts and rock mass subject to
variable stress state, rock mass quality and the presence of rock fractures or joints. It was
found that the bearing plates can improve the reinforcing performance of rockbolts.
Keywords: FLAC model; Rockbolt elements; Fully grouted rock bolts; Push tests;
Underground roadway.
1. Introduction
Rockbolts are used as primary reinforcement to strengthen the jointed/fractured rock mass in
civil and mining engineering excavations. Windsor (1997) categorised the current
reinforcement devices into three fundamental classes: Continuous Mechanically Coupled
* Corresponding author: Tel.: +61 2 42214492
E-mail address: [email protected]
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(CMC), Continuous Frictionally Coupled (CFC) and Discretely Mechanically or Frictionally
Coupled (DMFC). The fully encapsulated rockbolt system belongs to CMC, while expansion
shell bolts belong to the DMFC system and the Swellex and Split set rockbolts to the CFC
system. Because of the simple installation procedure, effective rock reinforcement and
economic factors, cement or resin grouted rockbolts are the most commonly used ground
reinforcement method.
The primary role of rockbolts is to restrain the rock mass deformation by providing resistance
to dilation and shear movement. This research is focused on the axial rockbolt behaviour only.
Cai (2004) indicated that the axial force distribution along a rockbolt has a significant
supporting effect and plays an important role in the design of the rockbolt pattern. Bjrnfot
and Stephansson (1984) indicated that rock mass quality can significantly influence the
behaviour of fully grouted rockbolts. The bond characteristics of the rockbolts are influenced
by the surrounding rock, the types of rockbolts and grout. Better understanding of the load
transfer mechanism between rockbolts and rock mass can lead to improved design of the
rockbolting system in the field. So far the rockbolt system design for underground roadways
in complex ground environments remains primarily empirical. Considering the difficulty and
cost of field monitoring, analytical and numerical models can provide alternative ways to
study the bolt loading behaviour.
A series of analytical solutions (Farmer, 1975; Li and Stillborg, 1999; Ren et al., 2010;
Blanco Martn et al., 2011; Ma et al., 2013) have been made to study the load transfer
mechanism in the rockbolting system. Farmer (1975) presented an analytical model to predict
the shear stress distribution of fully grouted rockbolts before decoupling occurs in the bolt-
grout interface. Li and Stillborg (1999) proposed a model for describing the behaviour of
rockbolts by dividing the rockbolt into elastic, softening and de-bonding zones. Ren et al.
(2010) and Blanco Martn et al. (2011) presented analytical models for fully grouted
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rockbolts based on a tri-linear bond-slip model. Ma et al. (2013) introduced a non-linear
bond-slip model to analytically simulate the behaviour of fully grouted rockbolts. However,
these analytical models have difficulty in representing the true interaction between rockbolts
and the in situ rock mass as the solutions are based on simplified bolt-collar loading
experiments.
Indraratna and Kaiser (1990) presented an analytical method to model the behaviour of a
circular tunnel supported by fully grouted rockbolts and Osgoui (2010) improved this model
to obey the non-linear Hoek-Brown yield criterion rather than the Mohr-Coulomb linear
failure criterion. The limitations of the analytical models by Indraratna and Kaiser (1990) and
Osgoui (2010) are:
a) Bearing plates were not taken into account.
b) The bolts were assumed as rigid meaning that any point along the rockbolt
experiences the same displacement.
c) The shear bond stress was not defined in appropriate way. To model the interfacial
shear stress distribution of the fully grouted rockbolt, the rockbolt was mechanically
divided into a pick-up length and an anchor length, on either side of the neutral point.
The neutral point position was determined by an empirical equation.
d) These analytical models were proposed for a circular tunnel and therefore may not be
easily applied to rectangular roadways due to a different stress distribution.
Hyett (1996) encouraged the use of numerical packages in reinforcement design if these
numerical methods are capable of simulating the fully grouted rockbolts. FLAC2D is
established on explicit finite difference formulation and supplies structural elements
representing the soil and rock support system. FLAC have seven specified types of structural
support elements: beam elements, liner elements, cable elements, pile elements, rockbolt
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elements, strip elements and support members. Rockbolt elements were selected in this study
due to their capability of modelling the strain-softening behaviour of the material between the
structural elements and the grid (Itasca, 2006). Although FLAC2D is a two dimension model,
it can still accurately represent the three-dimensional effect of the rockbolt interaction with
rock. Rockbolt elements are two-dimensional and interact with the FLAC grid through
coupling springs, which are nonlinear connectors that transfer forces and motion between the
rock bolt elements and the grid at the rockbolt element nodes.
Although rockbolt elements or the cable bolt elements provided by FLAC software are
popular in modelling the rockbolts in the field (Gale et al., 2004; Mark et al., 2007; Liu et al.,
2008; Hsiao et al., 2009), they cannot feature the interfacial shear bond softening mechanism
between the bolt and the rock mass when used without being modified. According to the
study of Ren et al. (2010); Blanco Martn et al. (2011) and Ma et al. (2013) the shear bond
stress between the rockbolt element and the grid/rock mass varies nonlinearly with the
relative displacement between the rockbolt node and the FLAC grid as shown in Fig. 5.
Hence, the FLAC code requires modifications in order to allow for adjusting the interfacial
shear bond stress along the bolt as a function of relative shear displacement. The behaviour of
fully encapsulated rockbolts as normally installed in underground coal mine roadways was
modelled using the FLAC2D rockbolt element that was modified by incorporating the FISH
(a programming language embedded within FLAC) to enable a non-linear bondslip
relationship that was derived experimentally. The effect of face plates, rock mass quality and
the occurrence of the rock joint was taken into consideration. Once the underground roadway
geology, stress state and rockbolt bond characteristics are known, the model can be used to
study the behaviour of mine roadways.
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To obtain the bond-slip relationship along the bolt-grout interface, a series of push tests were
conducted and the results implemented in the FLAC model to simulate the rock bolts in
underground roadways.
2. Laboratory push tests of short encapsulated rock bolts
The load transfer capacity of fully encapsulated resin-grouted rockbolts is influenced by resin
types and installation methods. A series of push tests were carried out at the University of
Wollongong (UOW) to study the bond characteristics. Owing to the difficulty of installing a
roof bolt at a mining face and then removing the bolt for testing in a laboratory, steel tubes
were introduced to provide a suitable substitute.
Several rockbolts were installed into steel tubes using a standard bolt installation procedure
for fully encapsulated rock bolts. The steel tubes were 1.7 m long with an internal diameter of
28.5 mm and a wall thickness of 9 mm. One end of the steel tubes was welded to a square
steel base plate while the other end was closed with the cap. The steel tubes were installed
vertically into a 64 mm diameter hole drilled into the mine roof, then removed and brought to
the laboratory for testing. The tubes with the installed bolts are as shown in Fig.1.
The installed rock bolts were cut into 15 sections, each 100 mm in length and numbered as
illustrated in Fig.2. The outer 200 mm long section near the collar of the hole was not fully
encapsulated because of the lack of resin. The load transfer of the individual 100 mm long
bolt sections was tested by pushing the bolt out of the tube using the Instron universal test
machine. The test setup is shown in Fig.3. During the push test, the loading force and the
displacement were recorded for each tube section. The load and displacement relationships of
the bolt 10 are shown in Fig.4.
Each tube section along the rockbolt had a distinct load-displacement curve, indicating that in
reality the shear bond capacity is not constant along the bolt. This was caused by several
factors including capsule film gloving, entrapped air bubbles and resin mix times. Additional
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results were reported by Hillyer et al. (2013). Since the rockbolts were installed following the
standard procedure, the experiments closely represent the practical behaviour of the rockbolts
in the field. However, past laboratory experiments showed that the short encapsulation
rockbolt push tests were approximately 25% higher than the pull tests (Aydan, 1989). Aziz
(2004) reported a 10% difference of the load bearing capacity in push and pull tests. In this
study the rockbolt push tests were implemented as the pull tests would have been impractical
due to the bolt specimen length.
Benmokrane et al. (1995) and Blanco Martn et al. (2011) proposed that grouted rockbolts in
short encapsulation could be employed to derive the relationship of the interface between the
rockbolt and the medium as long as the embedment length was short enough to ensure a
uniform distribution of shear stress. The shear stress distributes uniformly along the 100 mm
long section and hence the load-displacement curves can be treated as the fundamental
relationship for the rockbolt-grout interface.
The obtained load-displacement relationships can be converted to bond stress versus slip
relationships and the bond strength ( ) of one section can be calculated using the following
equation (Littlejohn and Bruce, 1975):
Ld
P
b = (1)
where L is the encapsulated length; bd is the diameter of rockbolt; P denotes the push load on
the loaded bolt end.
Bolt 10 shown in Fig. 1 was selected as an example and used in the following study. Bond-
slip curves were implemented into the FLAC model and the bolt behaviour was modelled
under various situations. Three representative bond-slip curves (section K, L and N) derived
from push tests are illustrated in Fig. 5.
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3. Introduction of rockbolt elements in FLAC2D
Rockbolt elements in FLAC2D were introduced by Ma et al. (2013) to simulate non-linear
behaviour of rockbolts due to their capacity of modelling the strain-softening behaviour of
the material between the structural element and the grid material (Itasca, 2006).
The shear behaviour of the rockbolt/grid interface is modelled by a spring-slider system at the
rockbolt nodal points. The interfacial shear behaviour during the relative displacement
between the structural rockbolt nodes and the grid is a function of the coupling spring shear
stiffness (cs_sstiff shown in Fig. 6b) (Itasca, 2006):
)( mpsstiffS uucsL
F= (2)
where: SF denotes the shear force that develops in the shear coupling spring; sstiffcs is the
coupling spring shear stiffness (in FLAC: cs_sstiff); pu refers to the axial displacement of the
rockbolt; mu is the axial displacement of the medium (soil or rock); L is the contributing
element length.
The maximum shear force is correlated to the cohesive strength of the interface and the
frictional resistance along the interface. The maximum shear force per length of the rockbolt
can be calculated as follows:
perimetercscsL
FsfricCscoh
S += )tan('max
(3)
where: scohcs = cohesive strength of the shear coupling spring (in FLAC: cs_scoh); '
C = mean
effective confining stress normal to the rockbolt element; sfriccs = friction angle of the shear
coupling spring (in FLAC: cs_sfric); perimeter = exposed perimeter of the element.
The shear force per rockbolt length, namely cs_scoh in FLAC, can be correlated to the
relative shear displacement. User-defined table cs_sctable links the shear coupling-spring
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cohesion (cs_scoh) to the relative shear displacement. Hence, the shear bond along the
rockbolt element can be described as a function of shear displacement using cs_sftable,
providing a way of adding an existing bond-slip curve in a FLAC model. In this paper, the
shear force in Eq. (3) is a function of cs_scoh, which is independent of the friction angle
properties (cs_sfric) and cs_sfric were hence set to zero.
The bond-slip was then implemented into the rockbolt element by cs_sctable, defining the
relationship between shear force divided by the contributing element length and displacement.
According to the definition, cs_scoh is the cohesive strength of the shear coupling spring
(with the unit of force/rockbolt length), which can be expressed as:
bdscohcs =_ (4a)
and hence, shear stress can be computed as follows:
bd
scohcs
_= (4b)
where bd is the diameter of rockbolt; denotes the shear stress along the rockbolt.
Therefore, bond-slip curves of 100 mm sections of rockbolt 10 were transferred into the
relationships of shear force per length versus displacement by Eq. (4a).
4. FLAC simulation of rockbolts
A numerical pull out test was conducted on the FLAC rockbolt model. The diameter of the
rockbolt was 22 mm while Youngs modulus of rockbolt steel and the tensile strength were
210 GPa and 335 kN respectively. The rockbolt properties used are shown in Table 1.
Table 1 Rockbolt properties used in FLAC model
Cross-
sectional area
(m2)
Elastic
modulus
(Pa)
Perimeter
(m)
cs_sstiff
(N/m/m)
Tensile yield
strength
(N)
3.8E-04 2.10E+11 0.069 5.00E+9 3.35E+5
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To simulate one rockbolt (say rockbolt No.10), the FLAC model of the rockbolt consisted of
17 elements, which is schematically shown in Fig. 7. Rockbolt elements 1 to 17 represent the
sections of A to Q shown in Fig.2. Each rockbolt element was assigned its corresponding
distinct bond-slip relationship by the user-defined table cs_sctable. Based on the previous
discussions, zero bond characteristics were input into the two rockbolt elements close to the
hole collar (namely rockbolt elements 16 and 17 shown in Fig.7). The pull-out velocity of 1e-
6 m/step was applied at the end of the bolt (node 18). All FLAC model grid points were fixed
in both the x and y directions.
4.1 Evaluation of the FLAC2D model
The coupling spring shear force and shear displacement of rockbolt elements 11, 12 and 14
(corresponding to section K, L and N in Fig. 2) were monitored and compared with the input
bond-slip relationships. Because of the long encapsulation, the tensile strength of the rockbolt
was set to a large value of 3.35109 N to ensure adequate displacement for each section and
to prevent the yield of the rockbolt in the test. The obtained value of the shear force was
transferred to shear stress by Eq. (4b). The comparison of the calculated and the input bond
slip curves for these three rockbolt elements are shown in Fig. 8. As can be seen in Fig. 8, the
FLAC model agrees well with the input bond-slip experimental relationships. The FLAC
model can successfully represent the local non-linear behaviour of rockbolts, which is
capable of simulating the reaction of rockbolts under different situations.
4.2 Rockbolt pull-out test
A tensile strength value of 335 kN was assigned to rock bolt 10, which was pull tested until
failure. The load-displacement was recorded and shown in Fig. 9. The bolt reached its tensile
strength of 320 kN. During pull testing the loaded end moved approximately 2.5 mm. The
axial force and shear force distribution in the FLAC model are illustrated respectively in Fig.
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10 and Fig. 11. It can be seen that the axial force was mobilised only in the section close to
the collar. As shown in Fig. 11 the shear force along the bolt-rock interface at the rockbolt
elements 16 and 17 is zero as this portion of the bolt was not encapsulated.
5. Simulation of the interaction between rockbolt and rock mass
In underground mines, once the roadway is excavated, the surrounding rock mass will
potentially move towards the roadway, causing roadway closure (roof lowering, floor heave
and lateral rib closure). The installation of rockbolts aims to improve the inherent self-
supporting rock strength. The axial force in the bolt and the interfacial shear stress along the
bolt depends on the rock mass deformation. After being installed, rockbolts work together
with the reinforced rock mass (Deb, 2006) and provide a resistance to rock mass deformation.
Because of the roadway opening, the rock mass close to the excavation is displaced more
than the interior rock mass. Rockbolts play a role in force being transmitted from the exterior
rock to the interior, which is done via the shear stresses at the rockbolt-grout interface (Sun,
1984). Based on in situ observations, Sun (1984) proposed that the deformation of the rock
mass eventually leads to three distinct zones developed along a rockbolt; neutral point, pick-
up length and anchor length. The relative displacement between the rock and the bolt is zero
at the neutral point, where the shear bond stress at the bolt-grout interface is zero while the
axial force reaches the maximum value. The section between the collar and the neutral point
is defined as the load pick-up part (Indraratna and Kaiser, 1990; Li and Stillborg, 1999) while
the length between the neutral point and the free end of the rockbolt forms the anchoring part.
In the simulation, the non-linear Hoek-Brown failure criterion is employed to model the
surrounding rock mass of the roadway in an underground mine. The Hoek-Brown criterion is
an empirical strength relationship, having the capacity of describing a non-linear increase in
strength of rock with increasing confining pressures. After several years of improvement, the
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latest version of the failure criterion (Hoek et al., 2002) provides an effective method to
predict rock mass properties based on laboratory measurements and field observations.
Eberhardt (2012) recommended that the Hoek-Brown criterion can be used for most rock
types (igneous, sedimentary and metamorphic) under various confinements.
The latest expression of the Hoek-Brown criterion (Hoek et al., 2002) is:
a
ci
bci sm )('
3'
3
'
1 ++=
(5)
where: '
1 and '
3 are the major and minor effective principal stresses at failure; ci is the
uniaxial compressive strength of the intact rock material.
The parametersbm , s and a in Eq. (5) are semi-empirical, which are related to Geological
Strength Index (GSI). GSI can be estimated directly from charts based on the overall rock
mass structure and the surface conditions of the discontinuities.
The coefficientsbm , s and a are the function of GSI described by:
)1428
100exp(
D
GSImm ib
= (6)
)39
100exp(
D
GSIs
= (7)
)(6
1
2
1 3/2015/ += eea GSI (8)
In Eq. (6) and Eq. (7), a factor D is introduced to describe the degree of disturbance caused
by blast damage and stress relaxation.
When rock mass surrounding the excavation reaches its residual (post-peak) strength, the
Hoek-Brown failure criterion can be expressed as:
'
)( ''
'
3'''
3
'
1
a
ci
bci sm ++=
(9)
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Parameters bm' , 's , 'a are the residual strength of bm , s , a and ci' is the residual uniaxial
compressive strength of the intact rock ci .
An attempt has been made to study the interaction mechanism between rockbolts and rock
mass which were simulated by rockbolt elements in FLAC and the Hoek-Brown material,
respectively.
The numerical model geometry and the applied boundary conditions of a roadway are
presented in Fig. 12. Because of the model symmetry only half of the roadway was simulated.
The FLAC grid size representing strata in the region of interest was 50 mm by 50 mm and the
simulated roadway dimensions were 5.5 m by 2.5 m. The FLAC rockbolt model proposed
here was adopted. The fully grouted rockbolts were labelled as shown in Fig. 12.
The Hoek-Brown constitutive model in FLAC was used. Two types of rock mass (GSI=35
and GSI=50) were adopted, where GSI=35 indicates rock mass folded and/or faulted with
angular blocks formed by many intersecting discontinuity sets and GSI=50 represents
interlocked, partially disturbed rock mass with multifaceted angular blocks formed by four
or more discontinuity sets (Hoek et al., 2002). The constant im was set as 10 and 12 for rock
mass GSI=35 and GSI=50, respectively. Table 2 illustrates the material parameters adopted
from Osgoui (2010) and used in the FLAC roadway model. The densities of these two
different types of rock mass were considered the same and set as 2000 kg/m3. Rockbolt
behaviour under various conditions (four models) was simulated and is detailed in Table 3. In
the Model 4, a horizontal joint was created in the roof to model the discontinuous rock mass.
Table 2. Geomechanical parameters of rock mass used in FLAC model, after Osgoui (2010).
Parameter GSI=35 GSI=50
Poisson's ratio 0.25 0.25
Deformation Modulus E (GPa) 2.57 9.34
Shear Modulus G (Gpa) 1.028 3.736
Intact rock strength ci (MPa) 30 60
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Residual intact rock strength ci' (MPa) 24 48
Disturbance Factor D 0 0
HoekBrown constant im 10 12
HoekBrown constant bm 0.981 2.012
HoekBrown constant bm ' 0.615 0.841
HoekBrown constant s 7.30E-04 3.87E-03
HoekBrown constant 's 1.70E-04 2.57E-04
HoekBrown constant a 0.516 0.505
HoekBrown constant 'a 0.538 0.530
Table 3. Variable conditions used in FLAC model
FLAC
Model
Parameters
xx
(MPa)
yy
(MPa) zz
(MPa)
P0 (MPa)
P1 (MPa)
Rock
mass
GSI
Face plate
Joint
Model 1 -6 -4 -5 -4 -6 35 No No
Model 2 -6 -4 -5 -4 -6 50 No No
Model 3 -6 -4 -5 -4 -6 50 Yes No
Model 4 -6 -4 -5 -4 -6 50 Yes Yes
5.1 Model 1-Roadway with GSI=35
In this model, stress tensor xx = -6 MPa, yy = -4 MPa and zz = -5 MPa was initialised
throughout the model grid and the boundary stress P0 = -4 MPa and P1 = -6 MPa (Fig. 12) and
rock mass with GSI=35 was adopted. Rock bolts were installed after the roadway was
excavated. The results are illustrated in Fig. 13. Rockbolt 2 in Fig. 13 has a distinctive
behaviour because it yielded during the modelling. The axial force distribution along rockbolt
1 is shown in Fig. 14, which is comparable to the measurements obtained by Gale, et al.
(1992), as shown in Fig. 15. As can be seen, all three rockbolts developed the neutral point,
the pick-up length and anchoring length; the direction of shear stress for the anchor length
and the pick-up length is opposite, which confirms the field observations of Sun (1984).
Rockbolts 1 and 3 have different axial force and shear force distribution as well as the
different neutral position. It can be concluded that the neutral position depends on the spot
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where the rockbolt is installed, implying that rockbolt behaviour is influenced by the
surrounding stress conditions.
5.2 Model 2-Roadway with GSI=50
In Model 2, rock mass was set to GSI=50 and all other settings were kept the same as in
Model 1. The only difference between Model 1 and Model 2 is the rock mass quality, the
objective of which is to study the influence of the rock mass properties on the behaviour of
the rockbolt. Fig. 16 shows the results of Model 2. Rockbolt 1 in Model 2 was chosen as a
representative to compare with the rockbolt 1 in Model 1 and its shear force and axial force
distribution is shown in Fig. 17. It can be seen that the shear and axial forces distribute in
different ways along the bolts between Model 1 and Model 2. For the rockbolts in Model 2, a
large neutral section exists instead of a single point indicating that rockbolts displace together
with the surrounding rock mass along these sections. The discrepancy of neutral point
locations between Model 1 and Model 2 agrees with the rock mass characteristics affecting
the rockbolt behaviour (Cai et al., 2004).
5.3 Model 3-The effect of bearing plates
Gray (1998) stated that bearing plates prevent the nut or forged head at the end of the
rockbolt from being pulled into the rockbolt hole. Nitzsche and Haas (1976) proposed that
the application of bearing plates will help strengthen the fractured rock mass near the collar.
It is believed that the rockbolt with a plate behaves differently from the one without a plate.
The purpose of Model 3 is to research the effect of bearing plates as Models 1 and 2 did not
account for bearing plates. Bearing plates were simulated by increasing the load transfer
between the last rockbolt element and the surrounding strata at the collar of the hole. Models
2 and 3 had the same rock mass properties and stress boundary conditions as detailed in Table
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3. The behaviour of rockbolts with plates (Model 3) was compared with the profiles of
rockbolts without plates (Model 2) and shown in Fig. 18.
In Fig. 18, it is clear that rockbolts with bearing plates still have neutral points, and even
under the same geological and stress conditions, rockbolts with plates tend to have higher
axial load and shear load. Rockbolts with plates can restrain the deformation of rock more
effectively resulting in higher axial force generated in the rockbolts. Face plates can also
influence the neutral point location. As can be seen in Fig. 18, the rock bolts with and without
plates have distinctive pick-up length, anchor length and neutral point positions. Rockbolts
with plates experienced additional load and hence, the bolt pick-up length is calculated in
order to establish the force equilibrium state.
In addition, the mine roadway in the Model 3 experienced smaller roof convergence than in
the Model 2 as shown in Table 4, which further confirms that the bearing plates can increase
the reinforcement effect of rockbolts.
Table 4 The Roof convergence of bolt 1 and 2 in Model 2 and 3
Roof convergence (mm) Bolt 1 Bolt 2
Model 2 6.84 7.37
Model 3 6.13 5.89
5.4 Model 4-Jointed roof
Rock joints were simulated by placing an interface 0.8 m above the roof. The axial force and
shear force distributions of the two roof bolts are shown in Fig. 19. As can be seen, the axial
force reached the maximum value at the joint intersection, decreasing gradually away on
either side. This was caused by the displacement and subsequent dilation along the joint.
Because of the peak axial force generated within the rockbolt at the joint location, the bolts
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failed before the whole roadway model reached the force equilibrium state. Hence, the results
shown in Fig. 19 were produced prior to rockbolt failure.
Hyett et al. (1996) stated that a higher reinforcement load would develop in discontinuous
rock mass than in a continuous rock mass. Models 3 and 4 hold the same setting parameters
except for the existence of the roof joint in Model 4. When Model 3 and 4 were both loaded
at the same rate, the rockbolts in Model 3 were still intact but the axial forces in rockbolts
reinforcing the joint (Model 4) have exceeded the bolt strength.
The modelling shows that delaying the installation of rockbolts after the roadway excavation
can cause a lower axial force in bolts and hence prevent the damage to rock bolts; however, it
would weaken the overall supporting performance of rockbolts. A similar conclusion was
also proposed by Cai et al. (2004) based on an analytical model.
6. Conclusions
Rockbolts were modelled by the FLAC rockbolt elements by taking into account the bond-
slip relationship of the bolt-grout interface that was derived from the laboratory short
encapsulation bolt push tests. The laboratory tests provide the practical solution to
investigation of the rockbolt behaviour in contrast to the field pull-out tests that are often
subjected to many variables.
Simulations of a mine roadway reinforced by the proposed rockbolt model were conducted to
predict the behaviour of rockbolts, from which the derived conclusions are:
a) Due to the difference in deformation between the exterior rock mass and the interior
rock mass, pick-up length and anchor length are formed along the rockbolts;
b) Rock mass quality can impact on the axial force and interfacial shear force
distribution along the rockbolts as well as the position of the neutral point;
c) Bearing plates can improve the reinforcing performance of rockbolts;
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d) Peak axial stress can be developed at rock joints which can lead to the rupture of the
rockbolts.
The factors such as the bond characteristics of rockbolt-grout interface, rock mass properties
and in situ conditions, need to be carefully considered when bolting design is undertaken. The
proposed FLAC model in this paper is capable of simulating the practical response of
rockbolts in the field. To reach a realistic simulation of underground roadway reinforcement
systems, the proposed numerical model should be built on the knowledge of the bond-slip
relationship of the bolt-grout interface and the field monitoring data. These include the stress
state around the roadway, rock mass quality, the occurrence of rock joints or faults and other
related factors.
This paper provides engineers with valuable tools to understand the axial behaviour of the
rockbolts reinforcing underground rock mass and to optimise the design of the rockbolt
pattern.
References:
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Engineering. Nagoya University, Nagoya.
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Figure captions:
Fig. 1 Steel tubes with stalled rockbolts
Fig. 2 The 100 mm rockbolt tube sections
Fig. 3 The push test setup
Fig. 4 Load-displacement relationships of sections along bolt 10
Fig. 5 Bond-slip relationships of section K, L and N of bolt 10
Fig. 6 Behaviour of shear coupling springs of rockbolt element (Itasca, 2006)
Fig. 7 Rockbolt elements, element numbers and node numbers
Fig. 8 Comparison of bond-slip curves for three bolt sections (K, L and N) with the input
bond-slip relationship
Fig. 9 Modelled load-displacement of rockbolt 10
Fig. 10 Modelled axial force distribution along the rockbolt when P=320 kN
Fig. 11 Modelled shear force distribution along the rockbolt when P=320 kN
Fig. 12 Numerical model of reinforced roadway with fully grouted rockbolts.
Fig. 13 Interfacial shear force and axial force distribution along the bolts in Model 1
Fig. 14 Interfacial shear and axial forces distribution along the bolt 1 in Model 1
Fig. 15 Axial force developed in rock bolt for various face advance positions, after Gale, et al.
(1992)
Fig. 16 Interfacial shear force and axial force distribution along the bolts in Model 2
Fig. 17 Interfacial shear force and axial force distribution along the bolt 1 in Model 2
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Fig.18 The comparison of the rockbolts with plates and without plates
Fig. 19 Axial force and shear force distributions of rockbolts for Model 4
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Fig. 1 Steel tubes with stalled rockbolts
117x118mm (96 x 96 DPI)
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Fig. 2 The 100 mm rockbolt tube sections
230x45mm (127 x 128 DPI)
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Fig. 3 The push test setup
141x76mm (96 x 96 DPI)
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diff
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om th
e fin
al o
ffici
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ersio
n of
reco
rd.
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Fig. 4 Load-displacement relationships of sections along bolt 10 224x155mm (96 x 96 DPI)
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may
diff
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ffici
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Fig. 5 Bond-slip relationships of section K, L and N of bolt 10 194x155mm (96 x 96 DPI)
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ompo
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n. It
may
diff
er fr
om th
e fin
al o
ffici
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reco
rd.
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Fig. 6 Behaviour of shear coupling springs of rockbolt element (Itasca, 2006) 230x113mm (96 x 96 DPI)
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ompo
sitio
n. It
may
diff
er fr
om th
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ffici
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reco
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Fig. 7 Rockbolt elements, element numbers and node numbers
139x117mm (96 x 96 DPI)
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ditin
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d pa
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ompo
sitio
n. It
may
diff
er fr
om th
e fin
al o
ffici
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n of
reco
rd.
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Fig. 8 Comparison of bond-slip curves for three bolt sections (K, L and N) with the input bond-slip relationship
213x157mm (96 x 96 DPI)
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uscr
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ditin
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d pa
ge c
ompo
sitio
n. It
may
diff
er fr
om th
e fin
al o
ffici
al v
ersio
n of
reco
rd.
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Fig. 9 Modelled load-displacement of rockbolt 10 194x155mm (96 x 96 DPI)
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uscr
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ditin
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d pa
ge c
ompo
sitio
n. It
may
diff
er fr
om th
e fin
al o
ffici
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ersio
n of
reco
rd.
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Fig. 10 Modelled axial force distribution along the rockbolt when P=320 kN 202x199mm (96 x 96 DPI)
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ditin
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d pa
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ompo
sitio
n. It
may
diff
er fr
om th
e fin
al o
ffici
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ersio
n of
reco
rd.
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Fig. 11 Modelled shear force distribution along the rockbolt when P=320 kN 206x194mm (96 x 96 DPI)
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ditin
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d pa
ge c
ompo
sitio
n. It
may
diff
er fr
om th
e fin
al o
ffici
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ersio
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reco
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Fig. 12 Numerical model of reinforced roadway with fully grouted rockbolts. 270x189mm (96 x 96 DPI)
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ditin
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d pa
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ompo
sitio
n. It
may
diff
er fr
om th
e fin
al o
ffici
al v
ersio
n of
reco
rd.
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Fig. 13 Interfacial shear force and axial force distribution along the bolts in Model 1 282x115mm (96 x 96 DPI)
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d pa
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ompo
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n. It
may
diff
er fr
om th
e fin
al o
ffici
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ersio
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reco
rd.
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Fig. 14 Interfacial shear and axial forces distribution along the bolt 1 in Model 1 222x146mm (96 x 96 DPI)
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ditin
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d pa
ge c
ompo
sitio
n. It
may
diff
er fr
om th
e fin
al o
ffici
al v
ersio
n of
reco
rd.
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Fig. 15 Axial force developed in rock bolt for various face advance positions, after Gale, et al. (1992) 115x106mm (96 x 96 DPI)
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man
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d pa
ge c
ompo
sitio
n. It
may
diff
er fr
om th
e fin
al o
ffici
al v
ersio
n of
reco
rd.
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Fig. 16 Interfacial shear force and axial force distribution along the bolts in Model 2 278x136mm (96 x 96 DPI)
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man
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ditin
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d pa
ge c
ompo
sitio
n. It
may
diff
er fr
om th
e fin
al o
ffici
al v
ersio
n of
reco
rd.
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Fig. 17 Interfacial shear force and axial force distribution along the bolt 1 in Model 2 215x137mm (96 x 96 DPI)
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ccep
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man
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py e
ditin
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d pa
ge c
ompo
sitio
n. It
may
diff
er fr
om th
e fin
al o
ffici
al v
ersio
n of
reco
rd.
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Fig.18 The comparison of the rockbolts with plates and without plates 224x330mm (96 x 96 DPI)
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d pa
ge c
ompo
sitio
n. It
may
diff
er fr
om th
e fin
al o
ffici
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ersio
n of
reco
rd.
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Fig. 19 Axial force and shear force distributions of rockbolts for Model 4 241x218mm (96 x 96 DPI)
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reco
rd.
University of WollongongResearch Online2014
Simulation of fully grouted rockbolts in underground roadways using FLAC2DShuqi MaJan NemcikNaj AzizPublication Details
Simulation of fully grouted rockbolts in underground roadways using FLAC2DAbstractKeywordsPublication Details